Download or read book The Math Encyclopedia of Smarandache type Notions written by Marius Coman and published by Infinite Study. This book was released on with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: About the works of Florentin Smarandache have been written a lot of books (he himself wrote dozens of books and articles regarding math, physics, literature, philosophy). Being a globally recognized personality in both mathematics (there are countless functions and concepts that bear his name) and literature, it is natural that the volume of writings about his research is huge. What we try to do with this encyclopedia is to gather together as much as we can both from Smarandache’s mathematical work and the works of many mathematicians around the world inspired by the Smarandache notions. We structured this book using numbered Definitions, Theorems, Conjectures, Notes and Comments, in order to facilitate an easier reading but also to facilitate references to a specific paragraph. We divided the Bibliography in two parts, Writings by Florentin Smarandache (indexed by the name of books and articles) and Writings on Smarandache notions (indexed by the name of authors). We treated, in this book, about 130 Smarandache type sequences, about 50 Smarandache type functions and many solved or open problems of number theory. We also have, at the end of this book, a proposal for a new Smarandache type notion, id est the concept of “a set of Smarandache-Coman divisors of order k of a composite positive integer n with m prime factors”, notion that seems to have promising applications, at a first glance at least in the study of absolute and relative Fermat pseudoprimes, Carmichael numbers and Poulet numbers. This encyclopedia is both for researchers that will have on hand a tool that will help them “navigate” in the universe of Smarandache type notions and for young math enthusiasts: many of them will be attached by this wonderful branch of mathematics, number theory, reading the works of Florentin Smarandache.
Download or read book Smarandache Semigroups written by W. B. Vasantha Kandasamy and published by Infinite Study. This book was released on 2002-12-01 with total page 95 pages. Available in PDF, EPUB and Kindle. Book excerpt: Generally, in any human field, a Smarandache Structure on a set A means a weak structure W on A such that there exists a proper subset B in A which is embedded with a stronger structure S.These types of structures occur in our everyday life, that?s why we study them in this book.Thus, as a particular case:A Smarandache Semigroup is a semigroup A which has a proper subset B in A that is a group (with respect to the same binary operation on A).
Download or read book THE PSEUDO SMARANDACHE FUNCTION written by David Gorski and published by Infinite Study. This book was released on with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Pseudo-Smarandache Function is part of number theory. The function comes from the Smarandache Function.
Download or read book Smarandache pseudo CI algebras written by L. C. Ciungu and published by Infinite Study. This book was released on 2022-01-01 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we define the notion of Smarandache pseudo-CI algebras and we investigate their properties. We also define and study the notions of Smarandache filters, pseudo-CI Smarandache homomorphisms and modal Smarandache operators on pseudo-CI algebras. The classes of Smarandache fantastic, implicative and positive implicative filters of Smarandache pseudo-CI algebras are defined and studied by extending some results regarding Smarandache fantastic, fresh and clean ideals in Smarandache BCI-algebras and Smarandache BCH-algebras to the case of Smarandache pseudo-CI algebras. The notion of Smarandache commutative pseudo-CI algebras is defined and a characterization theorem is given. It is proved that in the case of commutative Q-Smarandache pseudo-CI algebras the notions of Smarandache filters and fantastic filters coincide.
Download or read book SMARANDACHE NUMBERS REVISITED written by A.A.K. MAJUMDAR and published by Infinite Study. This book was released on 2018 with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt: More than seven years ago, my first book on some of the Smarandache notions was published. The book consisted of five chapters, and the topics covered were as follows : (1) some recursive type Smarandache sequences, (2) Smarandache determinant sequences, (3) the Smarandache function, (4) the pseudo Smarandache function, and (5) the Smarandache function related and the pseudo Smarandache function related triangles. Since then, new and diversified results have been published by different researchers. The aim of this book to update some of the contents of my previous book, and add some new results.
Download or read book Smarandache Fuzzy Algebra written by W. B. Vasantha Kandasamy and published by Infinite Study. This book was released on 2003 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author studies the Smarandache Fuzzy Algebra, which, like its predecessor Fuzzy Algebra, arose from the need to define structures that were more compatible with the real world where the grey areas mattered, not only black or white.In any human field, a Smarandache n-structure on a set S means a weak structure {w(0)} on S such that there exists a chain of proper subsets P(n-1) in P(n-2) in?in P(2) in P(1) in S whose corresponding structures verify the chain {w(n-1)} includes {w(n-2)} includes? includes {w(2)} includes {w(1)} includes {w(0)}, where 'includes' signifies 'strictly stronger' (i.e., structure satisfying more axioms).This book is referring to a Smarandache 2-algebraic structure (two levels only of structures in algebra) on a set S, i.e. a weak structure {w(0)} on S such that there exists a proper subset P of S, which is embedded with a stronger structure {w(1)}. Properties of Smarandache fuzzy semigroups, groupoids, loops, bigroupoids, biloops, non-associative rings, birings, vector spaces, semirings, semivector spaces, non-associative semirings, bisemirings, near-rings, non-associative near-ring, and binear-rings are presented in the second part of this book together with examples, solved and unsolved problems, and theorems. Also, applications of Smarandache groupoids, near-rings, and semirings in automaton theory, in error correcting codes, and in the construction of S-sub-biautomaton can be found in the last chapter.
Download or read book Smarandache Notions Journal Vol 13 written by Jack Allen and published by Infinite Study. This book was released on 2002-12-01 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: The books are published by Smarandache Notions Journal. It is an electronic and hard-copy journal of research in mathematics. Besides this, occasionally It publishes papers of research in physics, philosophy, literary essays and creation, linguistics, and art work. Initially the journal was called "Smarandache Function Journal". Since 1996 to present the original journal was extended to the "Smarandache Notions Journal". It is annually published in the United States by the American Research Press in 1000 copies and on the internet.
Download or read book Smarandache Function Journal vol 10 1999 written by V. Seleacu and published by Infinite Study. This book was released on with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of papers concerning Smarandache type functions, numbers, sequences, inteqer algorithms, paradoxes, experimental geometries, algebraic structures, neutrosophic probability, set, and logic, etc.
Download or read book n Fold Filters in Smarandache Residuated Lattices Part II written by Somayeh Motamed and published by Infinite Study. This book was released on with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we introduce the notions of n-fold BL-Smarandache n-fold BL-Smarandache fantastic filter and n-fold BL-Smarandache easy filter in Smarandache residuated lattices and study the relations among them. And we also introduce the notions of n-fold Smarandache n-fold Smarandache fantastic BL-residuated lattice and n-fold Smarandache easy BL-residuated lattice and investigate its properties.
Download or read book Smarandache Non Associative Rings written by W. B. Vasantha Kandasamy and published by Infinite Study. This book was released on 2002 with total page 151 pages. Available in PDF, EPUB and Kindle. Book excerpt: Generally, in any human field, a Smarandache Structure on a set A means a weak structure W on A such that there exists a proper subset B in A which is embedded with a stronger structure S. These types of structures occur in our everyday's life, that's why we study them in this book. Thus, as a particular case: A Non-associative ring is a non-empty set R together with two binary operations '+' and '.' such that (R, +) is an additive abelian group and (R, .) is a groupoid. For all a, b, c in R we have (a + b) . c = a . c + b . c and c . (a + b) = c . a + c . b. A Smarandache non-associative ring is a non-associative ring (R, +, .) which has a proper subset P in R, that is an associative ring (with respect to the same binary operations on R).
Download or read book Smarandache Notions Vol 14 written by W. B. Vasantha Kandasamy and published by Infinite Study. This book was released on 2004-01-01 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: Papers concerning any of the Smarandache type functions, sequences, numbers, algorithms, inferior/superior f-parts, magic squares, palindromes, functional iterations, semantic paradoxes, Non-Euclidean geometries, manifolds, conjectures, open problems, algebraic structures, neutrosophy, neutrosophic logic/set/probability, hypothesis that there is no speed barrier in the universe, quantum paradoxes, etc. have been selected for this volume. Contributors are from Australia, China, England, Germany, India, Ireland, Israel, Italy, Japan, Malaysia, Morocco, Portugal, Romania, Spain, USA. Most of the papers are in English, a few of them are in Spanish, Portuguese, or German.
Download or read book Groupoids and Smarandache Groupoids written by W. B. Vasantha Kandasamy and published by Infinite Study. This book was released on 2002-12-01 with total page 115 pages. Available in PDF, EPUB and Kindle. Book excerpt: Definition:Generally, in any human field, a Smarandache Structure on a set A means a weak structure W on A such that there exists a proper subset B in A which is embedded with a stronger structure S.These types of structures occur in our everyday life, that?s why we study them in this book.Thus, as a particular case:A Smarandache Groupoid is a groupoid G which has a proper subset S in G such that S under the operation of G is a semigroup.
Download or read book Smarandache Notions Vol 10 written by V. Seleacu and published by Infinite Study. This book was released on 2000-08-01 with total page 211 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Smarandache Unsolved problems and New Progress in Chinese language written by Editors: Liu Yanni, Li Ling, Liu Baoli and published by Infinite Study. This book was released on 2008 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: New improved results of the research in Chinese language on Smarandache¿s codification used in computer programming, smarandacheials, totient and congruence functions, sequences, irrational constants in number theory, multi-space and geometries.
Download or read book Smarandache Function Journal vol 12 2001 written by Charles Ashbacher and published by Infinite Study. This book was released on with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of papers concerning Smarandache type functions, numbers, sequences, inteqer algorithms, paradoxes, experimental geometries, algebraic structures, neutrosophic probability, set, and logic, etc.
Download or read book Smarandache Function Journal vol 7 1996 written by V. Seleacu and published by Infinite Study. This book was released on with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of papers concerning Smarandache type functions, numbers, sequences, inteqer algorithms, paradoxes, experimental geometries, algebraic structures, neutrosophic probability, set, and logic, etc.
Download or read book Smarandache Function Journal vol 14 2004 written by Sabin Tabirca and published by Infinite Study. This book was released on with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of papers concerning Smarandache type functions, numbers, sequences, inteqer algorithms, paradoxes, experimental geometries, algebraic structures, neutrosophic probability, set, and logic, etc.
